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Matematicheskie Zametki, 2007, Volume 81, Issue 3, Pages 328–334
DOI: https://doi.org/10.4213/mzm3675 (Mi mzm3675) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Asymptotic Behavior of Eigenvalues of the Laplace Operator in Infinite Cylinders Perturbed by Transverse Extensions

V. V. Grushin

Moscow State Institute of Electronics and Mathematics
Full-text PDF (445 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm3675
Abstract: We present sufficient conditions for the existence of an eigenvalue of the Laplace operator with zero Dirichlet conditions in a weakly perturbed infinite cylinder in the case of localized perturbations which are extensions along the transverse coordinates with coefficients depending on the longitudinal coordinate. If such an eigenvalue exists, then, for this eigenvalue, we obtain an asymptotic formula with respect to a small parameter characterizing the values of extensions.
Keywords: Laplace operator, eigenvalue, asymptotics, small parameter, infinite cylinder, localized perturbations.
Received: 13.12.2005
English version:
Mathematical Notes, 2007, Volume 81, Issue 3, Pages 291–296
DOI: https://doi.org/10.1134/S0001434607030029
Bibliographic databases:
UDC: 517.958
Language: Russian
Citation: V. V. Grushin, “Asymptotic Behavior of Eigenvalues of the Laplace Operator in Infinite Cylinders Perturbed by Transverse Extensions”, Mat. Zametki, 81:3 (2007), 328–334; Math. Notes, 81:3 (2007), 291–296
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm3675
  • https://doi.org/10.4213/mzm3675
  • https://www.mathnet.ru/eng/mzm/v81/i3/p328
    • This publication is cited in the following 2 articles:
    1. Bikmetov A.R., Gadyl'shin R.R., “On local perturbations of waveguides”, Russ. J. Math. Phys., 23:1 (2016), 1–18  crossref  mathscinet  zmath  isi  scopus
    2. V. V. Grushin, “Asymptotic Behavior of the Eigenvalues of the Schrödinger Operator in Thin Closed Tubes”, Math. Notes, 83:4 (2008), 463–477  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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